Quantum computing promises to improve the speed and scalability of computations over that of classical computing hardware. At this early stage of quantum computer hardware development, software frameworks which support rapid prototyping of quantum solutions on small-scale hardware or simulators are necessary to explore the application of quantum algorithms to hard computational problems. We present a software library, “QxLib,” which incorporates symbolic computation of optimization functions for quantum annealers as one means to enable rapid prototyping. We demonstrate its effectiveness on integer linear programming and integer factorization problems.
Quantum computing promises to improve the speed and scalability of computations over that of classical computing hardware. At this early stage of quantum computer hardware development, software frameworks which support rapid prototyping of quantum solutions on small-scale hardware or simulators are necessary to explore the application of quantum algorithms to hard computational problems. We present a software library, “QxLib,” which incorporates symbolic computation of optimization functions for quantum annealers as one means to enable rapid prototyping. We demonstrate its effectiveness on integer linear programming and integer factorization problems.
While quantum computing proposes promising solutions to computational problems not accessible with classical approaches, due to current hardware constraints, most quantum algorithms are not yet capable of computing systems of practical relevance, and classical counterparts outperform them. To practically benefit from quantum architecture, one has to identify problems and algorithms with favorable scaling and improve on corresponding limitations depending on available hardware. For this reason, we developed an algorithm that solves integer linear programming problems, a classically NP-hard problem, on a quantum annealer, and investigated problem and hardware-specific limitations. This work presents the formalism of how to map ILP problems to the annealing architectures, how to systematically improve computations utilizing optimized anneal schedules, and models the anneal process through a simulation. It illustrates the effects of decoherence and many body localization for the minimum dominating set problem, and compares annealing results against numerical simulations of the quantum architecture. We find that the algorithm outperforms random guessing but is limited to small problems and that annealing schedules can be adjusted to reduce the effects of decoherence. Simulations qualitatively reproduce algorithmic improvements of the modified annealing schedule, suggesting the improvements have origins from quantum effects.
With the emergence of D-wave’s quantum annealing machine, the power of quantum computing has become tangible, and the development of quantum computers is accelerating rapidly. Unfortunately, at present, the minimum value search that D-wave’s quantum annealing machine can handle is limited to quadratic functions of binary integer variables. This constraint is due to both hardware and software limitations. If this constraint was to be lifted, it would undoubtedly bring about a revolution in the world. Therefore, in this study, we obtained the basic mathematics of using quantum annealing, which enables hyper-parallel computing using qubits, to find the global minimum of any minimum value problem. Furthermore, we conducted simple simulations using classical computers to demonstrate the effectiveness of the ideas and algorithms. Furthermore, we conducted simple simulations using classical computers to demonstrate the effectiveness of the ideas and algorithms. We obtained also the mathematical method of using quantum annealing in learning neural networks and solving linear equations.
The area of quantum computing is a relatively new and promising branch of computation that hopes to provide help especially in the field of non-deterministic polynomial hard problems. Due to the fact that quantum computers are a heuristically non-binary approach to computation, based on the effects of quantum mechanics, a bunch of advantages and disadvantages come with it. The following work focuses especially on so-called quantum annealers, a special architecture of quantum computers that one can see as an application-specific unit that is using certain quantum mechanical effects to target binary quadratic optimization problems of the class of non-deterministic polynomial-time problems and tries to solve them faster than classical computers can do. Because this is a whole new area, it lacks extensive software support which is addressed in this work. Hence the majority of the thesis aims to develop and extend software that enables users to solve problem instances on a quantum annealer fast and reliable. Furthermore, the necessary steps to solve combinatorial optimization problems are explained and the necessary background of quantum physics theory is given. In conclusion, the main question of this work can be described as follows: 'Is it possible to create an automated pipeline to solve problems on a D-Wave Systems n.d. quantum annealer?'.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
Abstract Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a software architecture for compiling quantum programs from a high-level language program to hardware-specific instructions. We describe the necessary layers of abstraction and their differences and similarities to classical layers of a computer-aided design flow. For each layer of the stack, we discuss the underlying methods for compilation and optimization. Our software methodology facilitates more rapid innovation among quantum algorithm designers, quantum hardware engineers, and experimentalists. It enables scalable compilation of complex quantum algorithms and can be targeted to any specific quantum hardware implementation.
Quantum annealing is a form of quantum computing that exploits quantum effects to probabilistically solve a specific, NP-hard problem: finding the ground state of a classical, Ising-model Hamiltonian. Because physical quantum annealers are already available, there exists the pressing question of how to program such systems. That is, how can one map a computational problem into the coefficients of an Ising-model Hamiltonian for solution by quantum-annealing hardware? In this article, we address that question primarily from a practical standpoint. We survey extant software tools intended for programming D-wave annealing-based quantum processors and examine the programming model and solution technique promoted by each tool in an attempt to showcase the variety of contemporary approaches to solving computationally challenging problems on an existing annealing-based quantum computer.